Every hardware architecture has its own somewhat unique instruction set (add ax, bx...) when you build a C++ code, the compiler turns it into a machine code specific to the system/architecture you are working on. So you have to customize and build your code for different architectures for it to work on them.

But What happens in java is, When you build it, it is compiled into a Byte code (as opposed to machine code). And the java virtual machine(JVM) interprets the Byte Code into an instruction that is understandable by the specific architecture you the program is running on. There is JVM for every major architecture and operating system so the code you write on windows will be interpreted and run on MAC-OS or linux without any source level modification by you. That is why Java is portable and that is where the Write Once Run Everywhere motto comes from

In C only the source code is portable, you have to recompile it on every target platform, given that a suitable C compiler exist. Also, if you access any library or operating system function it must exist on any platform where you want to run your program on.

The big deal in java is, that the language itself brings a lot of standard libarary functions with it, so you rarely need access to the operating systems api.

"writing a specific JRE for each platform" is not something you do everytime. Porting the JRE to a new platform is something you need doing only once. This task is generally done by the core maintainer/developers of the program and/or the platform. A lot of factors may come into play when deciding who and how the JRE would be ported. Among other things, it depends on the licensed it's published under (I hear Java is Open Source, so I guess anyone could do it). Funny anecdote, Steve Jobs made a big deal about not wanting to take care of the porting of Java on Mac, around a year ago.

The point is not how or who ports the JRE, but the fact that once it is ported, every Java application should now theoretically run easily on the new machine. In that sense, the JRE forms an abstraction layer, completely hiding the machine, allowing easy porting.

However, reality is not always pretty like this. I won't go as far as calling portability a "myth", but it's true that it's not so perfect. For instance, Java has a package called JNI that allows sending native calls, bypassing the JRE, thus preventing the perfect seamless portability, what Java fans like to call "Write once run everywhere".

As mentioned in the comments, C++'s approach to portability is different. On the one hand, it's a compiled language, and those binaries are almost always platform specific. So c++ executables will never be portable (unlike Java). On the other hand, porting the compiler can sometimes be enough. The community has found that by porting the compiler as well as some core libraries of the language, source codes (and not binaries) could be portable.

However, C++ is widely used in critical systems like compilers, kernels, real-time systems,embedded systems, ... There's a "low level" aspect of C++ that cannot be overlooked, when talking about portability.